Ben rolls four fair 10-sided dice, each numbered with numbers from 1 to 10. What is the probability that exactly two of the dice show a prime number?
Answer: The probability that a 10-sided die rolls a prime number is $\frac{4}{10}=\frac{2}{5}$ since the primes it can roll are 2, 3, 5, and 7. We can choose which dice show a prime number in $\binom{4}{2}=6$ ways. Then, there is a $\frac{2}{5}\cdot \frac{2}{5} \cdot \frac{3}{5} \cdot \frac{3}{5}=\frac{36}{625}$ chance that the chosen dice will actually roll a prime number and the other dice won't. Therefore, the total probability that exactly two dice show a prime number is $6 \cdot \frac{36}{625}=\boxed{\frac{216}{625}}$.